Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-19T08:13:23.598Z Has data issue: false hasContentIssue false

The Steiner point of a closed hypersurface

Published online by Cambridge University Press:  26 February 2010

Harley Flanders
Affiliation:
University College, London
Get access

Extract

Let C be a compact convex set in En, not necessarily containing interior points. The Steiner point of K has been defined (see Shephard [6]) as

Type
Research Article
Copyright
Copyright © University College London 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Gericke, H., “Über stützbare Flächen und ihre Entwicklung nach Kugelfunktionen”, Math. Zeitschrift, 46 (1940), 5561.CrossRefGoogle Scholar
2. Grünbaum, B., “Measures of symmetry for convex sets”, Proc. Symposia in Pure Math. VII, American Math. Soc. (1963), 233270, esp. 238ff.CrossRefGoogle Scholar
3. Grünbaum, B., Convex polytopes, Wiley & Sons, New York (forthcoming), ¬¬14.3, 14.4.CrossRefGoogle Scholar
4. Kubota, T., “Über die Sehwerpunkte der konvexen geschlossenen Kurven und Flächen”, Tóhoku Math. J., 14 (1918), 2027.Google Scholar
5. Sallee, G. T., “A valuation property of Steiner points”, Mathematika, 13 (1966), 7682.CrossRefGoogle Scholar
6. Shephard, G. C., “Approximation problems for convex polyhedra”, Mathematika, 11 (1964), 918.Google Scholar
7. Shephard, G. C., “The Steiner point of a convex polytope “, Canadian J. of Math. (to appear).Google Scholar
8. Steiner, J., Von den Krümmungsschwerpunkte ebener Curven, Journal fur die Beine und Angew. Math., 21 (1840), 3363, 101–122 (= Gesammelte Werke, Band 2 (1882), 99–159).Google Scholar
9. Su, B., “On Steiner's curvature-centroid”, Japan. J. of Math.”, 4 (1927), 195201.CrossRefGoogle Scholar
10. Chern, S. S., “A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds”, Annals of Math., 45 (1944), 747752.Google Scholar
11. Flanders, H., “Development of an extended exterior differential calculus”, Trans. American Math. Soc., 75 (1953), 311326, esp. 323 ff.CrossRefGoogle Scholar
12. Flanders, H., Differential forms (Academic Press: New York, 1963), esp. 3844, 112–126.Google Scholar
13. Chern, S. S., “Integral formulas for hypersurfaces in Euclidean space and their applications to uniqueness theorems”, J. of Math, and Mech., 8 (1959), 947955Google Scholar